Equivalence classes of block Jacobi matrices

Abstract:

The paper contains two results on the equivalence classes of block Jacobi matrices: first, that the Jacobi matrix of type $2$ in the Nevai class has $A_n$ coefficients converging to $\boldsymbol {1}$, and second, that under an $L^1$-type condition on the Jacobi coefficients, equivalent Jacobi matrices of types $1$, $2$ and $3$ are pairwise asymptotic.